ch21_p17 - 17. (a) If the system of three charges is to be...

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17. (a) If the system of three charges is to be in equilibrium, the force on each charge must be zero. The third charge q 3 must lie between the other two or else the forces acting on it due to the other charges would be in the same direction and q 3 could not be in equilibrium. Suppose q 3 is at a distance x from q , and L x from 4.00 q . The force acting on it is then given by () 33 3 2 2 0 4 1 4 qq qq F x Lx πε §· =− ¨¸ ©¹ where the positive direction is rightward. We require F 3 = 0 and solve for x . Canceling common factors yields 1/ x 2 = 4/( L x ) 2 and taking the square root yields 1/ x = 2/( L x ). The solution is x = L /3. The force on q is 2 3 22 0 14 . 0 0 . 4 q qq q F xL ε =+ π The signs are chosen so that a negative force value would cause
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